Abstract
Equilibrium behaviour in classical Statistical mechanics can be described in terms of probability measures (called Gibbs ensembles) on an appropriate phase space. In their simplest form the Gibbs ensembles correspond to systems lying in a bounded region of space. However, in order to study phenomena such as phase transitions it is necessary to consider infinite volume limits of these ensembles. The work of Dobrushin (1968 a), (1968 b), (1969), Lanford and Ruelle (1969) and Ruelle (1970) shows that these infinite volume limits, called Gibbs states, can be defined as the probability measures which are compatible with a given collection of conditional probabilities. These conditional probabiIities are defined in terms of the potential energy for the system being considered.
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References
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Preston, C. (1980). Construction of Specifications. In: Streit, L. (eds) Quantum Fields — Algebras, Processes. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8598-8_18
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